Sometimes people say that water is removed from clothes in a sps vob(nf+1ytmt26 /t*iel( szin dryer by centrifugal force throwing the water outward. What is wro(biote z/ ynvfl16st(t+ s2m *ng with this statement?

Will the acceleration of a car be the same when the car travels around a shary3)kfsoemfc1uw-n04x 7z c* ep curve at a constant 60 km/h as when it t4ck)0uxz7 f1-eceofw3*my n sravels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doek s*hcg, ic5z1s the car exert the greatest 5h* sgczc,ik1and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round vf+ y-gc9b +b)pj8azw yt 8;axc+7kgd. Which of these forces provides -tgb ;v )pjyw+ +8 d8k ag9cba+czfx7ythe centripetal acceleration of the child?

A bucket of water can be whirdq std x.uzwmhk; n.d/3u2nz w(dr;3*led in a vertical circle without the water spilling out, even at the toz /3.h m(zx.kn uq2wusdn ;tddr*3dw;p of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three controard28sr,jku. r i j4(rls in the car which can beru(ik2r.jd8r ,4j a sr used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hil3c2k3f yng;g; gl4 v8mvt nxc8l, as shown in Fig. 5–31. Hi;f;8xtvyn 3 83glv4 c cggknm2s sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundin)ow9erx9v a3 24(i rc*bs* duh ly2bybg a curve at high speed?

Why do airplanes bank whenau -ti7/ 8ttcn jhb1ckv;a. a+ they turn? How would you compute the banking angle given its speed and radius of taci vt+ /7-ajn.1 ;ta8b kthcuhe turn?

A girl is whirling a ball on a string around her head in a horizontal plane.hidg.2d4r k(t1gc9yb2: g v1s8c fsmg She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the 2(r 8 19gk:ss mg21chfid.y c v4gdtgbstring?

Does an apple exert a gravitationalld4,2c(t/ p1ey xoiwskz qe,6 force on the Earth? If so, how large a force? Consider aow4eclze k26,psd(ty,x1 i /qn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, sf j 8va8)j8hgin what ways would the Moon’s orbit behjvf g88as) 8j different?

Which pulls harder gravitationally, the Earth on the Mooovqp5 qo9/nh. n, or the Moon on the Earth? Which accelerates hq59op .vqno/ more?

The Sun's gravitational pull on the Earth is much larger than the mql r6*s)q4slMoon's. Yet the Moon's is mainly )s slr4 l6mq*qresponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wb7 ku( t9hor.rhat two effects are at work? Do they oppose each other rkoh9(t.7b ur?

The gravitational force2 6mijmtc1k7e on the Moon due to the Earth is only about half the force on the Moon due to jk67 i2 1metcmthe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars inp xm0fb47j v23it*wn5w+xcod its orbit around the Sun larger or smaller4fm7v dwinj2ot3x*b 0p 5 cx+w than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite ti 1qbga3vv 73+9(llyjhjlh( (a) toward the east or (b) toward the west? Consider the Earth’s rotata33ht7v l+l v(qj19l (gbhyijion direction.

When will your apparent weight be the g;j mj6p6n9yumreatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the gpm 6;muj9y6 njround?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long peri+rhvvo r5eub*j;s37s ods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walksu*rjvs boe h7+5rv3;ing on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “ftlbef/s)l, e/i(u.qe ree fall” or “apparent weightlessness” between stepq)f es.e(le/tb,li/u s.

The Earth moves faster in its orbit around the Sun in January than in ef dfqrh; z;. ka2t:,lJuly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a fact;2qr t ;ke,zh.laf :dfor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hr(o frt3 /(kbvy)mu*wm2z ux *ave a moon. Explain how this discovery enabled an estimate o u2*)3krbo m/(wmtyvurz (f*xf Pluto’s mass.

  The Sun's gravitational pull on the Earth is muc6s;x(ch ,f clrh larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side ofc(cx;s6rh f,l the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980o z:j8c)z4p wn $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around k nel3echzuo, 834kt5the Sun, and the net force exerted onk5e3unc 38hzl k4,toe the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0 ; 4r)jcoyvs vmow1gsh9*q- 9h-kg discus as it rotates uniformly in a horizor ssh9vqhg9oy) o-j vc1wm;*4ntal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sur+/etmi fiuz0y-l dq9 ,face, and circles the Earth a9, em zdtl-0qfii+ u/ybout once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speckl2..s oiajurg l.7h ;objet5 :-da-ak of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions .o5u: kheislj;- .b a- tgjrd7loaa2.per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a w nqxo:mf8* k(vertical circle of r :mo *qx(8nkfwadius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 105y1:d+h uxcag mwl3b. mee -,6p0-kg car can round a turn of radius 77 m on a ub g3.pl- e+mey1cmx6:adh w ,flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of staa-hh5r i nrzbs5pl)/ 3tic friction be between the tires and the road if a car is to round a level curve of radius 5irzp r)sa-3nl hh5 b/85 m at a speed of 95km/h ?   

  A device for training astronar1t a/5bx) cv5ikc 7h-lmm 0ww n/uaj4uts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If ilva4r w5x/ j w)/ncm k-h7a0tumc1b5the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of vaz3phekfmen0 9r-*ktq6 t w*t ,riable speed. When the speed of the turntable isqke3ntfew0 m9k 6-, rhtz*pt* slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travel :ql+nez6 pf*w/2cj,hkvf)w j ing when upside down at the top cj wzw62q,/+:ffh)e n jlkvp*of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded tcoi:ow-oxlk:q c 7 84wop of a hili - ol:k:co4 qoxwwc78l (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to maoc*7(6 +efihcoy li8cke for the passengers to feel “weightlesco 6*7hfi oicc+e l(y8s” at the topmost point?    rpm

  A bucket of mass 2.00, 78.qhl+nf8z-2ul3n+houds u bgf ib kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2uuoh8sh-z q3 bf 2nlg7n +ufl.bd ,i8+5.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if;zbck.6/mk dx g;hey)z m3 o l*mjp,d, a particle 9.00 cm from the axis of ropo ); /z3 mh*;mb,6ly., mkdjdgzkcxetation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pefovz 8ei vd* gzbe+b gxoda+; 477;u-fople are rotated in a cylindrically walled "room." (o4i d+8zxbfe 7ugdv o;g*e 7z;va+fb-See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a x2abjg +i4;uv frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass+ibuv2 x ;jga4 m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignorink3tf: c-dl+njg the weight of the ball which revolves on :-kltj3+ dcn fa string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radiu jx,t jf: nt(a9onn+ 9o7sbn)ks of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masseuab2; rc,l5tlc x9wxe y24 9xm.btal4s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive9i w r9q/ft7cqiu:9 mvb3wpe6 maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripeo9)ygl8vt t.f tal components of the net force exerted on the car (by the ground) in Example 5-8tygl9) vf 8o.t when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformrzjotj1e.m 2)tzd ujv +,o8q3ly from the pit area, going from rest to 320km/h in a semicircular arc with 2 ejj r8vo+.o)3j1umzz td qt,a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a h6q- pr qa:ygjx/nm*4fg+ hvw0orizontal circle of radius 2.90 m . At a particular in+ja :yp / vrg6qf*w0-nxm hq4gstant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2nfn-gm7;u;w i Earth radii) above the Earth’s surface if its7fgnwim -un; ; mass is 1350 kg.   

  At the surface of a certain planet, on7s1v*b 1:q7uvv uwg the gravitational acceleration g has a magnitude of o*buw s: uv7nvg71q1 v12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius iszn rb1nj- j)g0, h(o b8bod/tg 1.74 jt,)og-1hbdj nb (rb/0nzgo 8$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times t s;s)3cpkk9nh.w0vs that of Earth, but has the same mass. What is the acceleration due to gravphsv 3s. 0t9;c)kwsnk ity near its surface?   

  A hypothetical planet has a masfmu-/3*-4qwmw sajths 1.66 times that of Earth, but the same radius. What is g near3hqm m-f w-u /t*jsaw4 its surface?   

  Two objects attract each other gravitati ctthio9( t wg0fkp,g)e4ndx,2 u *me,onally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceler-cx.ntajs8 btxp ub6rf e7bln4h 6603 ation of gravity, at (a) 3200 mfax4r 0txb87 3nes6b ut .p-lj6hb6nc    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s c.yld4l+su r *h5f d3eienter to a point outside the Earth where thegravitational acceleration dulldi 4*s3. 5u+heydfr e to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed int5s ljadj 0 re25pbsl+)jpc4wa)vl::ou(8qq po a sphere about 1) : 0j (+e2b48lodj)svarpqcp plsl jqau55w: 0 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which ux6 21ckgp /uzb9eu1donce was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity d9uu ux1beg 2c61k p/zon this star?    $\times 10^7$

  You are explaining why astronaut 0i adxmzk2b 98f5 xp5x2y8txknu5 w1ts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was jd 9p imx08ux8n1ywxt55fk x 2z5aktb2ust a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 mv35xh4 /jdnb l. Calculate the magnitude and direction of the dn3j l/5xvhb 4total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thexvi ,5 qcv aizc ,g5z5m3x,s9 hjaqo38 planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all5h3ajc agzvq5vo3z,9 , i q8c,x5simx four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at u tgrdx:o*,m /the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 /dg xurtm :o,*km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of thenw-+fdiwm- +kct7 h(x Earth and its distance from the Sun. [Note: Compare your answer to that obtained usi7(km n++hww -dxictf- ng Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the n r c9i2u3v6prEarth n692ivcr3 urp at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circul,6ce w c91jqraar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release 961jw,cq race occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshl3*y.*ofs5 ajt1xa y xip rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Q5* f t.3xaxlj*o1 yyasuestion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to o3d6d h3ri6k izrbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the szkdr6 d3 i63ihatellite?    s ~    min

  At what horizontal velocity would a sate30o2ytthwyoekn g8 ( 7sbgn+-;8sh hullite have to be launched from the top of Mt. Everest to be placed in a circular orbit around3onhuskyt 0-hgw2+8to8h e7s( y ;bgn the Earth?   

  During an Apollo lunar l 2 3p:wet :ktq1gma6ptdz2:dnanding mission, the command module continued to orbit the Moon at an altitude of about 100 km. Hk::6 1dgp2qptda23 e w:m zttnow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit t5 :x6px8kuez/0pt+fs1 7cqvgm miwp0he planet. The inner i8pmmpefz7t0gku: 01qc6 / 5 +swxxvp radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diamet qt u0nqlnmm9zc32a;lt+ el82er rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom? le;mtqc2z9 3lnn8m+q2 la u 0t
(a)    (b)   

  What is the apparent wei*y 0ifl-og k1wtkd hm9: xr/9wght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a spa*fm1 i- r:gh9wkxlwk /ot 09dyce vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-stak;mo a 0l,xyy9r system consists of two stars of equal mass. They are observed to be separated by 360 million km and l9kym 0,o;yax take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring so ,+c:0sdy+fv8xawfu, o1 lj-f ycrt;cale read for the weight of a 55-kg woman in an elevator that movodjx :l,0a,u+w18y+f sv f; f r-tccyoes
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a fc4feglyp*m , 6 o4e(ucord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelfoe ,ecp fy(l4g46*u merates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits verf:7rng-;pbr5oiwv-c y near the surface of a planet with period T , the density (mass/volume) of the planet is fbp-57rw ;rg i-nc:vo$\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of (xm qh5 iji-t)kko2n :-hmpt* the Moon (27.4 d) to determine the period of an artificial satellite orbiting veq mhj( t)m ho5t2-ikxk p*-in:ry near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundqoh +2a dwk250p0r lcered meters across, orbits the Sun like the planets. Its period is 410 d. What i200w5dqp +l2krcha oe s its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4q;fvg 4a: tc.(jin iv8.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comesm ordb//:ws k; very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kb/od ;m/k:wrs epler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center)j(bi,cjf ss6 of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, andfq4ov -nkek:h7pa6c*v c1lg su(9z 6f mean distance for the four largest moons of J9ou4* zfh l ps vnf(1ea7qvk66g-kc :cupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earr-aqvos)q ):qth from the known period and distance of the Moon. : rq-v)soqq a)   $\times 10^{24}$

  Determine the mean ditxchf)w (h b6()fk0bxstance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Iow)h(6cfbkxthf (0 b)x and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragoew5a26-k/f +aisx l a,fi)czments (which some space scientists think came from a planet that once orbited the6 )o5fw/ is +ia2,a-c akezflx Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial z8 s4nh:vdgpf4q.qo *"planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Eartd4 84n .gh*pqf zvoq:sh. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by w k5 f)hd)vvr7swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can twdr5h)7 )v fkvolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gp .- )/k.ztwjy dowp-bravity be half what it is on the surfatwjyw.p kbo d/-.z)p-ce?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab a1d9fdbl6yn 4 hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and theibd9yn 4alf1d 6r individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration oag: 1u6 )emb m1ag*eucf gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimat 1abc*eu 1amggemu):6 e the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelin7g;vrv :ybj4lhi.7 l wg directly from the Earth to the Moon experier7;ylv w:jv. bglh7 4ince zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you spu s 25ftb34sc f(oq8 yb9il;utand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which di4oyff; p38st 25bqsblui9 (curection?     ----待选择----upwartddown 

  A projected space station consis3u (j*asp23socx xadg -dt ;2zts of a circular tube that will rotate about its center (like a tu *2usddaac-3sxgtox 3jzp ;2(bular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraf9 xz uax,yd6eg* /jeml8na3*rt in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mas cat2*vcp*cmt8 ftzx + / ycp;n9:ha/ds of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gra z np/d*a9fpc+2/:8mcc;ty *vxttcha vitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the lwdlnh*63z xrb 8os*; jaei+z4(4oil vertical by an anhjz6 (bd *rz losi8*4o 3l x+i;wneal4gle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If w9y73aghvw 0 rthe coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle9r3ww7v hay0g the curve?

  How long would a day be if the Earth werf*pb1e)xbi+g5l ma 7ee rotating so fast that objects at the equator were appare*lfm)ip b5+b xg71ea ently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a con578gfackr2 adw3zr dht0x7e2 ol 0ok.stant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a cu-ldq.:dgm ow8gg7vk q rck 5/2ob +/)ecsz:sd rve of radius 235 m. A lamp suspended from the ceiling swincz)d:kq ek8m7/ /g5gbldq s2v.soo-w dc+gr: gs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as ta3 1ix6m o2e yrzd5+zdhe Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the siz1e6z+miyr5 zd 3a2xo de of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Span 5hi;4lxf ;m,l kp3tzce Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the cfh ;mltlk4ni5p3;x z ,ore to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hiv1k/v;3 qx2nmyih. l ell and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car avk3nv1m l .2/yeqx;hit A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System ( iqbqza5g,8(n;c 6eifr1yu) oGPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an ac a,q;r8)og1 yzq cnefibi6 u(5curacy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km,b9.a ;-3bsefgxn rv0l is meant to orbit tn-f.lbvxgab 3r s0e;9 he asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle xn(xdgw5 +po2l(o3x qpursuing a satellite in need of repair. You are in a circular orbit of the same radius apxd2 g+olxoq53 (w(nxs the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yea+z(2u 6w1 fnym9ylj vcrs. (a) What is its mean distance from the Suyjz 6n(1lfc2w u9yvm +n?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuall 5o j2-zd9zwpv( n1djx9a m5kzy "feel" yourself gravitationallwd9jj(a mz-9 z v1od p5xz2k5ny attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a distarl *.(jl/szp dw/o2ovnce of about 30,000 light-years from the cen z/ o.w/pjd2ro*vl sl(ter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on f+oue)co ci pv:gg + 2(l,p8 ryyg-o/geach side. Find the mi :y(gu,-e 8+lov+oc/ fgg2oyp gr)pc agnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the .hq;**.nlp /bwrx gg aEarth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-longdh w4y 9sx)1zncxq)m 1 sweep second s)41q1z cxdwhxymn)9hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored o *vn+n5ydoqw (6(tvl and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle yonl*56+ q( ovd(wvnt that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a nebz nv4q9m/yl 7w highway is designed so that a car traveling at spzb /vn ml974qyeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tildh( z3 jym*5bpnou,1rt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accelera* p ,mbu15dyj( zorh3ntion, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$